1.) My first compound question would be (as it has been in the past),
"What are some good texts? And for what levels? (beginner, intermediate,
advanced?)"

For example, I've been eyeing the following two books since they're
commonly used, but of course, commonly used is not a guarantee they're
any good.

James Stewart 2011 Algebra and Trigonometry 3rd Ed ISBN:0840068131

James Stewart 2011 College Algebra Concepts and Contexts ISBN:0495387894

As usual with university texts, we're dealing with the variance in
"required material" and preferred teaching style for particular courses
along with the textbook mafia exploiting the differences in opinions
with multiple overlapping titles. I wouldn't quite call the multiple
versions of the same material "cut-and-paste textbooks," but they're
still really close.

Sure, I've got the luxury of revisiting fundamentals for fun even though
I don't necessarily need to revisit them again. As expected, when done,
I'll probably have my own uneducated opinion of how good those texts are
at teaching the basics, but that's beside the point -- You have the
clear advantage of having far more experience with math, and hence,
you'd have a much more informed opinion of good texts.

1.a) "Other references or resources besides textbooks?"

2.) My second question would be, "Why limit it to just `Linear Algebra`?"
This could be my own academic ignorance showing through or possibly a
language barrier of some sort, but there are so many different and
useful applications of "Algebra" that limiting it to a specific area
seems, well, overly confining and constrained.

If you're just trying to be humble and only stick to stuff you know
really well, I can empathize. There are a lot of smart math folks on HN,
and some of them know particular fields extremely well, so venturing
outside of your field of expertise can be a risky proposition. On the
other hand, I know you're damn good at a lot of different fields of
mathematics, so even if you aren't the resident expert of a particular
field, your insights can still be very useful and beneficial --A good
example is me asking you about textbooks even though I know you don't do
the whole regular teaching thing, let alone spend your time evaluating
each new edition and variation of books for the sake of potentially
using them in a class. If someone wanted to know more about the
application of Algebraic Theory to Automata Networks, your opinion is
still a hell of a lot more informed than mine. (And no, I don't really
understand it... yet!)

3.) If you want to stick to the topic of just Linear Algebra, "Where is
Linear Algebra useful?" The pure math folks are always amazing, but the
engineering types want to know how to apply the knowledge to do useful
work. The first step is simply knowing where things could be useful.

3.a) "Why is Linear Algebra useful in particular areas?"

The things you consider to be "completely elementary" or even blatantly
obvious, probably aren't. I'd bet the reason why this submission hasn't
resulted in a whole lot of questions is due to people being afraid of
looking dumb, publicly. Some of the knowledge you take for granted is
actually intimidating to others, or worse, they actually dreaded their
mathematics classes and try to avoid the topic out of fear.

http://24.media.tumblr.com/tumblr_l0z6j5sHtL1qz7s3bo1_500.jp...

> So, exactly what is it that you think you want to know about Linear Algebra?

If people don't know where Linear Algebra is applicable to do useful
stuff, they won't think of things that they want to know.

Without using a long string of expletives, I'm unable to express how
much more qualified you are than I am for giving answers to 3/3a.

4.) Lastly (and rhetorically), "Why do people tend to discount the
things they know?" --Even if learning math was easy for you, you still
put in a lot of effort, so you ought to give yourself more credit. :)